We review our investigations devoted to the analysis of the resonances Z(c)(3900), Z(c)(4430), Z(c)(4100), X(4140), X(4274), a(1)(1420), Y(4660), X(2100), X(2239), and Y(2175) discovered in various processes by Belle, BaBar, BESIII, D0, CDF, CMS, LHCb and COMPASS collaborations. These resonances are considered as serious candidates to four-quark (tetraquark) exotic mesons. We treat all of them as diquark-antidiquark states with relevant spin-parities, find their masses and couplings, as well as explore their dominant strong decay channels. Calculations are performed in the context of the QCD sum rule method. Thus, the spectroscopic parameters of the tetraquarks are evaluated using the two-point sum rules. For computations of the strong couplings GT(M1M2), corresponding to the vertices TM1M2 and necessary to find the partial widths of the strong decays T -> M1M2, we employ either the three-point or full/approximate versions of the QCD light-cone sum rules methods. Obtained results are compared with available experimental data, and with predictions of other theoretical studies.